Managing the Use of Insecticides in Agricultural Fields: A Modeling Study

A. Misra, A. Yadav
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Abstract

At present time, sustainable crop production is of prime importance due to the expansion of human population and diminishing cultivable land. Insects attack the plants’ roots, blooms and leaves and lessen the agricultural production across the globe. In this research work, we propose a nonlinear mathematical model to manage the spray of insecticides to control insect population and increase crop production. In the model formulation, we consider that the spraying of insecticides is attributed to both the density of insects and loss in crop production. This study identifies the range of spraying rate of insecticides at which the model system shows bistability behavior and its threshold value after which system stabilizes to the equilibrium with higher crop production. Further, we have also demonstrated that the model undergoes transcritical, saddle-node, Hopf, and Bogdanov–Takens bifurcations. The extensive numerical simulation is performed to validate the analytical findings.
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管理杀虫剂在农业领域的使用:一个模型研究
目前,由于人口的增长和可耕地的减少,可持续的作物生产是至关重要的。昆虫攻击植物的根、花和叶,减少了全球的农业产量。在本研究中,我们提出了一个非线性数学模型来管理杀虫剂的喷洒,以控制昆虫数量和提高作物产量。在模型公式中,我们认为杀虫剂的喷洒是由于昆虫的密度和作物生产的损失。本研究确定了模型系统表现出双稳定行为的杀虫剂喷洒量范围及其阈值,该阈值之后系统稳定到作物产量较高的平衡状态。此外,我们还证明了该模型经历了跨临界、鞍节点、Hopf和Bogdanov-Takens分岔。进行了广泛的数值模拟来验证分析结果。
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